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The authors develop an object-based rate control algorithm for MPEG-4 arbitrarily shaped video object coding. There are three main contributions. An improved quadratic rate-distortion model for texture information is derived, which is more accurate for arbitrarily shaped video objects. Secondly, an accurate rate-distortion model for shape information is introduced. Combining the rate-distortion models for texture and shape information, an object level rate control is proposed. To achieve constant bit rate, the quantiser is adjusted based on buffer fullness. The tradeoff between picture quality and buffer fullness is considered. Compared with the rate control algorithm for the MPEG-4 verification model, the proposed scheme can achieve a more stable buffer without sacrificing picture quality.